1. Field of the Invention
The present invention relates to a two-element fθ lens used for a micro-electro mechanical system (MEMS) laser scanning unit (LSU), and more particularly to a two-element fθ lens using an angular change varying with time in a sinusoidal relation for correcting a MEMS reflecting mirror having a simple harmonic movement to achieve the scanning linearity effect required by the laser scanning unit.
2. Description of the Related Art
At present, a laser scanning unit (LSU) used by a laser beam printer (LBP) controls a laser beam scanning by a high-speed rotating polygon mirror as disclosed in U.S. Pat. Nos. 7,079,171, 6,377,293 and 6,295,116 or TW Pat No. I198966, and principles of those inventions are described as the following: a semiconductor laser emits a laser beam through a collimator and an aperture to form parallel beams. After the parallel beams pass through a cylindrical lens, the beams are focused at the width of the X-axis in the sub scanning direction and along a direction parallel to the Y-axis of the main scanning direction to form a line image and projected onto a high-speed rotating polygon mirror. The polygon mirror includes a plurality of continuous reflecting mirrors disposed substantially at or proximate to the focusing position of the line image. The polygon mirror is provided for controlling the direction of projecting the laser beam, so that when a plurality of continuous reflecting mirrors are rotated at high speed, the laser beam projected onto a reflecting mirror can be extended in a direction parallel to the main scanning direction (Y-axis) at the same angular velocity and deviated from and reflected onto a fθ linear scanning lens. The fθ linear scanning lens is installed next to the polygon mirror and may be either a single-element lens structure (or a single scanning lens) or a two-element lens structure. The function of this fθ linear scanning lens is to focus a laser beam reflected by the reflecting mirror of the polygon mirror and projected onto the fθ lens into an oval spot that is projected onto a photoreceptor (or a photoreceptor drum, which is an image surface) to achieve the requirement of the scanning linearity. However, the traditional laser scanning unit (LSU) still has the following drawbacks in its practical use.
(1) The manufacture of the rotating polygon mirror incurs a high level of difficulty and a high cost, and thus increasing the manufacturing cost of the LSU.
(2) The polygon mirror requires a function of a high-speed rotation (such as 40000 rpm) and a high precision, and thus a cylindrical lens is required and installed to the traditional LSU since the width of the general polygon mirror along the Y-axis of the reflecting surface of the mirror is very thin, so that the laser beam pass through the cylindrical lens can be focused and concentrated into a line (or a spot on the Y-axis) and projected onto the reflecting mirror of the polygon mirror. Such arrangement increases the number of components and also complicates the assembling operation procedure.
(3) The traditional polygon mirror requires a high-speed rotation (such as 40000 rpm), and thus the noise level is raised. Furthermore, the polygon mirror takes a longer time to be accelerated from a starting speed to an operating speed, and thus increasing the booting time of the laser scanning.
(4) In the fabrication of the traditional LSU, the central axis of a laser beam projected onto the reflecting mirror of the polygon mirror is not aligned precisely with the central rotating axis of the polygon mirror, so that it is necessary to take the off axis deviation of the polygon mirror into consideration for the design of the fθ lens, and thus increasing the difficulty of design and manufacturing the fθ lens.
In recent years, an oscillatory MEMS reflecting mirror is introduced to overcome the shortcomings of the traditional LSU assembly and replace the laser beam scanning controlled by the traditional polygon mirror. The surface of a torsion oscillator of the MEMS reflecting mirror comprises a reflecting layer, and the reflecting layer is oscillated for reflecting the light and further for the scanning. In the future, such arrangement will be applied in a laser scanning unit (LSU) of an imaging system, a scanner or a laser printer, and its scanning efficiency is higher than the traditional rotating polygon mirror. As disclosed in the U.S. Pat. Nos. 6,844,951 and 6,956,597, at least one driving signal is generated, and its driving frequency approaches the resonant frequency of a plurality of MEMS reflecting mirrors, and the driving signal drives the MEMS reflecting mirror to produce a scanning path. In U.S. Pat. Nos. 7,064,876, 7,184,187, 7,190,499, 2006/0033021, 2007/0008401 and 2006/0279826 or TW Pat No. 253133, or JP Pat. No. 2006-201350, a MEMS reflecting mirror installed between a collimator and a fθ lens of a LSU module replaces the traditional rotating polygon mirror for controlling the projecting direction of a laser beam. The MEMS reflecting mirror features the advantages of small components, fast rotation, and low manufacturing cost. However, after the MEMS reflecting mirror is driven by the received voltage for a simple harmonic with a sinusoidal relation of time and angular speed, and a laser beam projected on the MEMS reflecting mirror is reflected with a relation of reflecting angle θ(t) and time as followsθ(t)=θs·sin(2πf·t)  (1)
wherein, f is the scanning frequency of the MEMS reflecting mirror and θs is the maximum scanning angle at a single side (symmetrical with the optical Z axis) after the laser beam passes through the MEMS reflecting mirror.
In the same time interval Δt, the corresponding variation of the reflecting angle is not the same but decreasing, and thus constituting a sinusoidal relation with time. In other words, the variation of the reflecting angle in the same time interval Δt is Δθ(t)=θs·(sin(2π·f·t1)−sin(2π·f·t2)), which constitutes a non-linear relation with time. If the reflected light is projected onto the target from a different angle, the distance from the spot will be different in the same time interval due to the different angle.
Since the angle of the MEMS reflecting mirror situated at a peak and a valley of a sine wave varies with time, and the rotating movements if a traditional polygon mirror are at a constant angular speed, if a traditional fθ lens is installed on a laser scanning unit (LSU) of the MEMS reflecting mirror, the angle of the MEMS reflecting mirror produced by the sinusoidal relation varied with time cannot be corrected, so that the speed of laser beam projected on an image side will not be an uniform speed, and the image on the image side will be deviated. Therefore, the laser scanning unit or the MEMS laser scanning unit (MEMS LSU) composed of MEMS reflecting mirrors has a characteristic that after the laser beam is scanned by the MEMS reflecting mirror, scan lights at different angles are formed in the same time. Thus, finding a way of developing a fθ lens (some prior art named as f-sin θ lens) for the MEMS laser scanning unit to correct the scan lights, such that a correct image will be projected onto the light, examples as, U.S. Pat. No. 7,184,187 provided a polynomial surface for fθ lens to adjust the angular velocity variation in the main-scanning direction only. However, the laser light beam is essential an oval-like shape of the cross section that corrects the scan lights in the main-scanning direction only may not be achieve the accuracy requirement. Since, a fθ lens with main-scanning direction correcting as well as sub-scanning direction correcting demands immediate attentions and feasible solutions.